Examinations by the inventors of the present invention have learned that measurement and control of pattern dimensions by the use of an electronic microscope exclusive for the measurement (length measuring SEM) is generally conducted today in the semiconductor manufacturing processes. The measurement of pattern dimensions has been automated by applying image processing technologies to acquired images of the length measuring SEM, and therefore, expert skills of operators have become unnecessary, and measurement variance due to the individual differences has been decreased. Objectives of such pattern measurement are mostly patterns of a resist, an insulating film, polysilicon and the like, and the width of wire, diameters of circular holes and so forth are measured.
An example of the measurement techniques is shown in FIGS. 14A, 14B and 14C. Image signals of the SEM is changed according to the pattern shapes and materials, and they shine brightly especially at edge portions of a pattern. FIG. 14 shows an example of processing a signal waveform of a wire shape pattern. In the signal waveform, two peaks with large signal amounts correspond to edge portions of the wire, and the edge positions are defined in the manner as shown in FIG. 14 so as to measure the dimensions of the objective pattern. The technique of FIG. 14A is a method to detect the maximum inclined position of a peak (maximum gradient method), FIG. 14B shows a threshold method to detect an edge position by the use of a specified threshold value (th), and FIG. 14C shows a linear approximation method in which a straight line is applied to an edge portion and a base portion and a point of intersection therebetween is detected.
In the prior dimension measurement method using the SEM images and image processing technologies as described above, peaks and positions of image signal waveforms and signal amounts or changes thereof are used to determine the positions to be measured. However, in these techniques, it is not possible to precisely grasp which portion an actually measured dimension corresponds to in an actual cross section (a top portion, a bottom portion or other of the pattern). Especially, in the case where a cross-sectional shape of the pattern changes, errors in dimensions to be measured become different depending on the cross-sectional shape of the pattern, which has been a problem with the prior art.
FIG. 15 shows an example of influences that the changes in cross-sectional shapes of the pattern give to the measurement, practiced in 2002 by Villarrubia et al. (Scanning electron microscope analog of scatterometry”, Proc. SPIE 4689, pp. 304-312). FIG. 15 shows an example of simulation illustrating the case where dimensions are measured by the threshold method (threshold value 50%), in which errors at the measured position and the actual bottom position in the cross section are different between the case where a pattern sidewall is vertical (left side of FIG. 15) and the case where it is inclined (right side of FIG. 15). Such positional difference comes from the fact that the measurement algorithm in the prior length measuring SEM does not consider how a signal waveform changes according to the differences of pattern cross-sectional shapes.
FIG. 16 shows relationships between the tilt angle of the pattern sidewall (horizontal axis of FIG. 16) and pattern dimension measurement errors (vertical axis of FIG. 16) by various image processing algorithms (max. Deriv., Regressiont, Sigmoid, Model-Based Lib.), and illustrates that the measurement errors change depending on cross-sectional shapes of the pattern and the algorithms. Along with the scaling down in the semiconductor manufacturing processes, influences that the measurement errors according to the pattern shapes give to the process control have become more and more significant. Therefore, it is necessary to solve such errors and realize dimension measurement with small errors. Further, for the achievement of higher precision in the process, it is required not only to realize the dimension measurement with small errors but also to realize the quantitative evaluations of errors in cross-sectional shapes as shown in FIG. 15.
In other words, as a technology for solving the technical problem concerning FIG. 15, Villarrubia et al. have proposed a measurement method using an electron beam simulation. This is a method in which signal waveforms in which errors in the cross section of the pattern are taken into consideration are generated by an electron beam simulation and thereby creating libraries, and the signal waveforms of actual SEM are compared with the waveforms in the libraries, and an actual cross-sectional shape of the pattern is estimated from similar waveforms, and then, the correct dimensions are calculated. The Model-Based Lib. in FIG. 16 is the evaluation result of the measurement errors, and a more precise measurement than other techniques can be achieved. In this way, by this technique, it is possible to reduce the measurement errors due to the cross-sectional shapes and to evaluate the cross-sectional shapes. However, it is required to prepare in advance the signal waveforms of SEM to various cross-sectional shapes as libraries. For highly precise measurement, it is necessary to prepare the libraries having a sufficient amount of data. As a result, the amount of data will become enormous and it will take much time to prepare libraries. Furthermore, in the measurement, the prepared waveforms must be compared with actual waveforms, and therefore, calculations take much more time than conventional measurement techniques. The present invention is one of other measurement techniques that requires relatively small calculation amount than the technique of them.